UMICH-2015: Response to Inflation Action Items

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Action Items: updated list, with names (November 2, 2015)

Start writing (making a strong case for r)

RF and SS will get started right away.

Prospects for r and nt for various configurations and values of r

(Fisher matrix forecasts including foregrounds that will feed into more detailed simulations)


Possibility to establish departure from scale invariance even for extended parameters space for both S3 and S4


Improvements on other inflationary observables (running, non-Gaussianity, etc. while varying neutrino mass/Neff)


Inflationary Models that CMB S4 could see hints for (e.g. modulated reheating)

The present best constraints on local non-Gaussianity come from the Planck 2015 analysis and give fNL = 0.8 ± 5.0 (68% CL) [Planck2015 - 1502.01592]. A noise-free cosmic variance limited CMB experiment is expected to produce constraints on fNL with 1-σ error bars of about 3 [astro-ph/0005036]. Therefore the best that can be expected of CMB Stage-IV is slightly less than a factor of two improvement on the current best limits.

A detection of local non-Gaussianity would have far reaching theoretical implications, since any significant detection of local fNL would rule out all models of single clock inflation [astro-ph/0407059]. In the absence of a detection, however, it is important to ask what can be learned from improved constraints on fNL. Though not firm, nor entirely robustly defined, it can be argued that a natural theoretical threshold where qualitatively new general conclusions about the physics of the early universe can be drawn would come from constraints on fNL<O(1), see for example [1412.4671] for a fuller discussion. In order to achieve this level of constraint, it seems necessary to move beyond the cosmic microwave background to study other data sets, such as large scale structure. Despite the fact that CMB Stage-IV is not expected to reach this threshold, it is worth asking what can be gleaned from an improved constraint on fNL from the CMB.

There do exist some well motivated models for the origin of fluctuations in the early universe which predict local non-Gaussianity at a level where CMB Stage-IV could either hint toward, or slightly disfavor at around the level of 2 σ. These models include the simplest modulated reheating scenario [astro-ph/0306006] and ekpyrotic cosmology [0906.0530], both of which predict f_NL~5.

In the modulated reheating scenario, the field which drives inflation φ decays to the particles of the standard model with a rate γ which is determined by the value of a second field σ which remains light throughout inflation. The quantum fluctuations in σ result in a spatially modulated reheating surface resulting in the curvature perturbations that we observe in the CMB and large scale structure. The process by which the fluctuations in the light field are converted into curvature fluctuations naturally results in local non-Gaussianity given by fNL = 5(1-ΓΓ″/Γ′2), where this formula holds in the case that φ oscillates about a quadratic minimum after inflation and the fluctuations in φ make a negligible contribution to the observed power spectrum.

This can be contrasted with the simplest curvaton scenario, where a field σ which remains light during inflation comes to dominate the energy density of the universe after the field which drives inflation φ decays. The fluctuations in the energy density of σ then determine the curvature perturbations that are observed today. The local non-Gaussianity in this simple model is predicted to be fNL = -5/4 [hep-ph/0110002], which is unfortunately a few times smaller than the expected error bar from CMB Stage-IV.

Absent a significant detection of local non-Gaussianity (which is unlikely given the current constraints from Planck), CMB Stage-IV can provide useful constraints or tantalizing hints about particular models of the early universe, though it will unfortunately be unable to reach the level of constraint at which broader conclusions can be drawn.

Dependence of error bars on lmin

Several observables display a dependence on lmin that motivates lmin=14. One example is the optical depth.


It is shown as a function of lmin for two values of the optical depth and two reionization histories. Parameters degenerate with it inherit the strong dependence. The reionization histories corresponding to the various curves are shown in the next plot. This is largely independent of the reionization history.


The multipole range that contains most of the information does not significantly depend on the reionization history but does depend on the optical depth. The effect of the different reionization histories on the angular power spectra is shown in the next plot.

Clee dzr.png

Science drivers that would affect design of experiment

Light axions with masses between 10^-33 eV and 4x10^-28 eV (not the QCD axion) would lead to an isotropic rotation by ~9 arcmin (independent of the axion decay constant). This would be rotated away by EB nulling. (The mass range is such that they oscillate between recombination and today, but not long before recombination).

The absolute polarization angles are currently typically calibrated to around 1 degree. To detect such axions or rule them out, one would have to calibrate the polarization angles at ~3 arcmin.

A very neat idea to achieve this goal was recently proposed in

Isocurvature forecasts

How should we parameterize?

Julien Lesgourgues

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